1.1.7.3 Deduction

Version 1.4 August 2016                                        (Previous Version)

The most famous example of logic is the following:

       If all persons are mortal and Socrates is a person then Socrates is mortal.

This is an example of a syllogism.  We often explain it this way:

Premise 1:                   All persons are mortal.

Premise 2:                   Socrates is a person.

Therefore:                   Socrates is mortal.

We can show this in a Venn diagram:

There is a set of persons. Socrates is a member of that set.  Socrates has the same attributes as other members of the set – including the attribute of being mortal.

There are many varieties of syllogisms.  Aristotle found 64 standard forms.  For instance:

If John is taller than Mary and Mary is taller than Tom then John is taller than Tom.

Taller than is a transitive relationship.  John, Mary and Tom are being ranked on one dimension.

But sometimes a rule that looks apparently the same doesn’t work in practice.  more

·       If John likes Mary and Mary likes Tom then John doesn’t necessarily like Tom.

We can't deduce that John likes Tom.  John and Tom may be rivals for Mary’s affection.

·       If Alice is the mother of Brenda, and Brenda is the mother of Claire, Alice isn't the mother of Claire.

"Is the mother of" is not a transitive relation.  Alice is Claire’s grandmother.

Universities run courses in logic – it applies in philosophy, mathematics, science and engineering.  The subject can appear to be horribly complex and overwhelming to those of us who aren’t mathematically minded.  The rules of logic are not always rigid – sets can be fuzzy, concepts vague, rules uncertain. 

Whether any rule of logic works in a situation or not depends on the nature of reality.  We have to understand on a case by case basis how the elements of any proposition are mapped onto reality.  With the most sophisticated forms of logic we still need to understand its connection to reality.

●  We have to know the attribute of “being mortalâ€� applies to all members of the set of persons.

●  We have to know “is taller thanâ€� is a transitive relation but “likesâ€� and “is the mother ofâ€� are not.

There are potentially different systems of logic.  In logic, pluralism is the view that there is no one correct logic, or alternatively, that there is more than one correct logic.  One may, for instance, believe that classical logic is the correct logic generally, but believe that paraconsistent logic is the correct logic for dealing with certain paradoxes. However, there are different versions of logical pluralism depending on what one believes 'logic' to be and what it means for a logical system to be 'correct'.  For our purposes, to work out some global beliefs so that we can determine global values and know how to behave, these possibilities are irrelevant.

We currently phrase our conclusion in this area as follows: